When you take a point of damage, put a damage chit on the rightmost free space on your robot's sheet.

When you're dealt program cards at the start of your turn, you get one less card for each damage on your robot.

Once you've taken enough damage, you start to suffer "locked registers". This means that some of your program cards get stuck and you're forced to use them even if you don't want to. Check the book for exact rules.

When you place the last (tenth iirc) chit, your robot explodes.

If a robot is destroyed from damage or a pit, then it respawns at its archive marker (the little cardboard squares with the robot's name on it) with two damage on it.

By default the archive is at your start spot, but if you land on a spanner space (including a flag) then you move your archive marker to that space.

Powering down:

This confuses absolutely everybody so I'll go into more detail than your question asked. No insult intented.

If you want to power down, you have to declare it while programming your robot at the start of a turn.

Take a power down marker and put it on your robot's sheet. Program your robot with five cards as normal. Your robot performs that turn as normal. It's not powered down yet.

At the end of the turn, your robot powers down. Remove all damage from it immediately. You spend the next turn powered down. While powered down you don't get any program cards to give to your robot; it won't move or even fire its laser. It just sits there brick-like. Unless it's on a conveyor belt or something (bad idea).

So in short, you can't power down mid-turn. If you take a bunch of unexpected damage, the best you can do is to declare a power down next turn and spend that turn trying to survive/getting to a safe place. At the end of that turn you heal, and spend the turn after that powered down.

Hope that's helpful.

Other misc Roborally rules queries that normally come up sooner or later:

You need to end your move on a flag to tag it, or on a spanner to place your archive marker there. You only benefit from the repair if you end your turn on it.

Curved-arrow conveyor belts only turn your robot if you're moved onto them by another conveyor.

It taught me that someone can show off cool, innovative and elegant central mechanic. But there's nothing to stop them overdeveloping it into a piece of mush. When he said he was designing the expansion sets to meet the stretch goals during the kickstarter campaign , that should have been the warning sign. They certainly didn't feel very playtested.

And it's been a while since I pushed the game to the back of the cupboard but I seem to remember we had a lot of problems where the cards didn't really say what they did. Without unambiguous wording on the card, we kept having to check the rulebook to find out what each phrasing meant. And sometimes the BGG forums.

Oh yeah - and the (much mentioned) atrocious packaging. The expansions were in carboard boxes so flimsy that they were shipped with elastic bands put round them to stop the cards falling out. Not only did this not work, but the boxes were so flimsy that they were destroyed by the elastic bands.

It was an educational experience and taught me some much-needed cynicism - in hindsight a bargain at twice the price.